Shellac based. BIN by Zinsser.

A good clean and a good sanding/abrasion (by hand) is always a good way to start something like this. TSP (trisodium phosphate) can be used to wash down the surface (it is a powerful degreaser which is why the building industry uses for cleaning surfaces).

Then rinse it with water-damp cloths a few times (2-3 rinses = removes the TSP residue leaving a clean surface) and allow to dry. Once dry (a few hours later) you can start the abrading (this is what sanding is called when you do NOT remove the finish but simply scratch it up). Once you have finished the abrasion, you can then go ahead and do another SLIGHTLY damp-cloth wipe down (removes the dust you just created). Allow to dry (another hour please).

Now you go ahead and prime with a very good primer (as Sophie has already suggested). Allow primer to cure (read the instructions ON LINE very, very carefully) and then TEST for adhesion. The "finger nail" test is excellent. Scratch at a corner with your finger nail. If the primer stays in place (no damage) you are GOOD TO PAINT.

If you can remove the primer with a finger nail, you have adhesion failure and need to start again.

Good luck.

Do not allow any well meaning worker at your favorite big box store to talk you into latex primer because it is easier and cheaper! The shellac primer is at least double the price and worth every penny